Affect of Spatial and Temporal Discretization in the Numerical Solution of One-Dimensional Variably Saturated Flow Equation

Affect of Spatial and Temporal Discretization in the Numerical Solution of One-Dimensional Variably Saturated Flow Equation

M. S. Islam

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R. Ahamad

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Shahjalal University of Science and Technology

Affect of Spatial and Temporal Discretization in the Numerical Solution of One-Dimensional Variably Saturated Flow Equation

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Abstract

Numerical simulation of the Richards’ equation in dynamically saturated soils keeps on being a difficult assignment because of its highly non-linear course of action. This is especially evident as soils approach saturation and the conduct of the principal partial differential equation changes from elliptic to parabolic. In this study, we developed a numerical model for solving Richards’ equation with regards to finite element approach in which pressure head-based scheme is proposed to approximate the governing equation, and mass-lumping techniques are used to maintain stability of the numerical simulation. Dynamic adaptive time stepping procedure is implemented in the Picard and Newton linearization schemes. The robustness and accuracy of the numerical model were demonstrated through simulation of two difficult tests, including sharp moisture front that infiltrates into the soil column with time dependent boundary condition and flow into a layered soil with variable initial conditions.

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Funding

No external funding was declared for this work.

Conflict of Interest

The authors declare no conflict of interest.

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No ethics committee approval was required for this article type.

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How to Cite This Article

M. S. Islam. 2020. \u201cAffect of Spatial and Temporal Discretization in the Numerical Solution of One-Dimensional Variably Saturated Flow Equation\u201d. Global Journal of Science Frontier Research - F: Mathematics & Decision GJSFR-F Volume 20 (GJSFR Volume 20 Issue F7).

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GJSFR Volume 20 Issue F7

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Crossref Journal DOI 10.17406/GJSFR

Print ISSN 0975-5896

e-ISSN 2249-4626

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GJSFR-F Classification MSC 2010: 37M15

Submission ReceivedSeptember 1, 2020
Peer Review Double Blind
Handling Editor
Accepted September 29, 2020
Published October 12, 2020

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v1.2

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November 23, 2020

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